Zero phase shift filter

ABSTRACT

A zero phase shift filter effective over a wide frequency range. It is made up of a dynamically bounded differentiator, acting as a lead network, together with an integrator, the overall circuit having a total phase shift approaching 0* over a frequency band up to 10 octaves.

United States Patent Sheldon L. Simmons Inventor [56] References CitedCahf- UNITED STATES PATENTS 1 5 No' 3 3 2 2 1969 3,322,970 5/1967Batteau 307 295 3,421,141 l/1969 Meyerhoff.... 328/167 x Paemed 1971 3465 276 9 969 8'1 328 155 x Assi The United States 61 Americ 1 gnee a asre resented b the Secreta 0 the Nay 3,466,552 9/ 1969 Sels 307/295 X p yY 3,529,245 9/1970 Single 328/127 Primary Examiner-John S. HeymanAt10rneysRichard S. Sciascia, Q. Baxter Warner and ZERO PHASE SHIFTFILTER "Ward Murray 4 Claims, 3 Drawing Figs.

U.S.Cl 1. 328/167, ABSTRACT: A zero phase shift filter effective over awide 328/127, 328/155 frequency range. It is made up of a dynamicallybounded dif- Int. Cl 1104b 15/00 ferentiator, acting as a lead network,together with an integra- Field of Search 328/155, tor, the overallcircuit having a total phase shift approaching 167, 127; 330/107, 109,124, 30 D; 307/295 0 over a frequency band up to l0 octaves.

3 W. I I R I l I 3 I H l E l I it i E o 2 l l I l LEAD N ETWORK 2OINTEGRATOR 22 PATENTEDIIEI I2 IsII 3.613.016

I4 IO I2 I I I INPUT SERVO-AMP SERVO- MOTOR LOAD I6 I8 VFEEDBACK I lLOOP FILTER POTENTIOMETER Fig.

RIZ

LEAD NETWORK 2O INTEGRATOR 22 Fig. 2 4

I I l l l I I I I I l I I I I I I INVENTOR SHELDON L. SIMMONS Fig. 3AGENT ZERO PHASE SHIFT FILTER STATEMENT OF GOVERNMENT INTEREST Theinvention described herein may be manufactured and used by or for theGovernment of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

BACKGROUND OF THE INVENTION In many electronic applications wherefilters are utilized an objectionable shift in phase occurs when theinput signal passes therethrough. If the phase of the signal conveys apart or all of the data, the filter output may not be trulyrepresentative of the information being conveyed.

One approach to the problem has been to employ a tracking filter, whichties the phase of the output signal to that of the input signal byfollowing the latter as it varies over the passband. However, not onlyare such tracking filters of complex design, but their cost is oftenprohibitive and in addition the possibility of a malfunction can notalways be tolerated.

Another expedient has been to employ linear filtering techniques, twofilters having phase variations in opposite sense being connected inseries in an attempt to compensate for the overall phase shift. However,it is found that the slope of the characteristic curve increases withdecreasing bandwidth, so that variations in phase cannot be overcomewithout adversely affecting the selective properties of the filteritself.

SUMMARY OF THE INVENTION The present concept combines a lead networkwith an integrator to form a lag-free filter especially suitable forincorporation into a servoloop in order to extend the comer frequency ofa servomotor while retaining a high gain at the low end of the passband.A feature of the concept resides in the attainment of controllable gainover a wide frequency range without introducing the instability and/orhigh noise conventionally associated with such control. An essentialfactor in the invention operation is the dynamic bounding of the outputdata as a continuous function of the input data.

OBJECTS OF THE INVENTION One object of the present invention, therefore,is to provide a filter having essentially zero phase shift over a widefrequency range.

Another object of the invention is to provide a zero phase shift filtermade up of a lead network and an integrator, the lead network acting asa dynamically bounded differentiator.

A further object of the invention is to provide a lag-free wide-bandfilter especially suitable for incorporation into a servoloop withoutintroducing instability or raising the noise level of the system.

Other objects, advantages, and novel features of the invention willbecome apparent from the following detailed description of the inventionwhen considered in conjunction with the accompanying drawings.

SHORT DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of a type inwhich the present concept finds particular application;

FIG. 2 is a schematic circuit diagram of one form of zero phase shiftfilter designed in accordance with a preferred embodiment of the presentinvention; and

FIG. 3 is a modification of one portion of the circuit of FIG. 2.

DESCRIPTION OF THE PREFERRED EMBODIMENT Although capable ofincorporation into a large number of electronic filtering applications,such for example as those found in data processors, analog simulatorsand computing networks, a filter designed according to the principles ofthe present invention is particularly suitable for employment in 'afeedback circuit to control the operation of a servomechanism is fedback to the input of amplifier 14 through a filter 16, the

T where amplitude of the feedback energy being controlled by some meanssuch as a potentiometer 18. In conventional networks of this type, thefilter 16 introduces an objectionable phase shift into the feedbacksignal passing therethrough, and it is a principal object of the presentinvention to improve system response by eliminating this objectionableshift in signal phase.

Conventional filters frequently utilized in electronic applicationsinclude the Bessel, Butterworth, Tchebyscheff, transversal, predictorand tapped delay line types. All of these possess inherent phase shiftwith frequency change. Three-pole Bessel filters are generallyconsidered to have superior minimization of such phase shift-minus 67.5at one octave above f,,.

Referring now to FIG. 2 of the drawings, it will be recognized that theparticular embodiment of the present invention there illustrated is madeup of two sections-a lead network 20 and an integrator 22. The conceptis based upon the principle that, for the lead network 20,

E 1 E I where E =output of network 20 E =input to filter and I I I rlFor the complete filter of Fig. 2

dc I EM-J; dt where E =output of the filter f( i) =.f( I 5 IE! Theessence of the present concept as exemplified by the circuit of Fig. 2is an ability to perform the operation by dynamic bounding (to bediscussed hereinafter) assures that the data-level-out will never exceedthe data-level-in.

Classical active-element differentiators have the following gain vs.frequency relationship:

e=Tpe, Such a differentiator, followed by an integrator with the typicalgain vs. frequency relationship of results in an overall gain vs.frequency relationship of PK PFfl Thus, in using the classicaldifferentiator with a classical integrator, no filtering (that is,amplitude attenuation as a function of data frequency changes) occurs.

When using the network of FIG. 2, however, the following relationshipholds:

/Tp) and the filter approximates the performance of a true integratorwithout the normal resultant phase lag. This results from the principleof dynamic bounding of the output signal.

Considering now the details of the lead network 20 of FIG. 2, it will beapparent that three parallel paths are provided for the input signal E,.One path includes an operational amplifier A in series with resistor Rthis combination being further in series with capacitor C resistor R anda further amplifier A A resistor R, shunts amplifier A and a capacitor Cshunts amplifier A Two diode-resistor combinations R,,D and Fi -D areconnected in parallel both with each other and with amplifier A,, asshown. The output terminal at which voltage E appears is betweenresistors R, and R,,,.

A secofii signal path includes an operational amplifier A in series withresistors R and R Shunting amplifier A is the parallel combination ofresistor R and diode D Similarly, a third signal path includesoperational amplifier A in series with resistors R and R the parallelcombination of resistor R, and diode D shunting amplifier A as broughtout in the drawing.

in operation, a signal e, applied to the input terminal flows throughthree paths respectively headed by resistors R R and R Amplifiers A, andA are half-wave rectifiers with precision gain characteristics. A is aninverting amplifier. The respective outputs of A and A provide voltagelevels for the dynamic bounding of the output data at E 0,;

C,, D D and A form a differentiatorTThe output of A, is continuouslylimited by A R R, and D as well as by A R R and D so that I E 0.1 S llon a dynamic basis.

The integrator 22 of FIG. 2 comprises the series combination of aresistor R and an amplifier A,, the latter being shunted by capacitor CThe output of the complete filter appears at E as illustrated.

The following exemplary values for the components of FIG. 2 have beenfound to be satisfactory in practice:

R R R R =l kilohm C,=0.003 pfd.

C =0.075 pfd.

A,, A A A A, operational amplifiers D,, D,, D D diodes When componentshaving these values are employed in the circuit of FIG. 2, a sine waveinput e, produces an insertion loss of 3 db. at 0.175 l-lz., and aninsertion loss of -26 db. at

10 Hz. Furthermore, the phase shift approaches zero over a frequencyrange from 0.1 to Hz.

Since the operation of the differentiator 20 can optionally be expressedas 0 it and is not restricted to e,,=e,, the arrangement of FIG. 2 maybe extended as shown in FIG. 3 of the drawings by the provision of afurther amplifier A capacitor C and resistor R incorporated into the twopaths respectively containing the amplifiers A and A In this circuit ofFIG. 3, K becomes l/RwC, and when such a differentiator is followed bythe integrator 22, the filter has the output characteristic E,,=( l/RwC)E, and possesses essentially zero phase shift.

I claim:

1. An electrical filter designed to pass with essentially zero phaseshift an input signal varying over a frequency band up to approximately10 octaves, said filter comprising:

a differentiating network receiving at least a portion of said inputsignal;

an integrator receiving the output of said differentiating network; and

means for dynamically bounding the output of said differentiatingnetwork as a continuous function of variations in said in ut signal, sothat the level of the data received by sai integrator does not exceedthe level of the data represented by the input signal variations.

2. An electrical filter according to claim 1 in which the means fordynamically bounding the output of said differentiating network includesa pair of half-wave rectifiers respectively forming part of two signalpaths each of which is connected in essentially parallel relationshipwith said differentiating network and each of which receives a portionof said input signal.

3. An electrical filter according to claim 2 in which each of the twosignal paths which includes one of said pair of halfwave rectifiers alsoincludes a parallel diode-resistor combination shunting the particularhalt wave rectifier included in that path.

4. An electrical filter according to claim 3, further including anamplifier, a series resistor R, and a capacitor C shunting saidamplifier, all of such further components forming a common part of eachof said two signal paths, whereby the output characteristic E, of thefilter becomes (l/RwC) E, where E, is the input signal to saiddifferentiating network.

1. An electrical filter designed to pass with essentially zero phaseshift an input signal varying over a frequency band up to approximately10 octaves, said filter comprising: a differentiating network receivingat least a portion of said input signal; an integrator receiving theoutput of said differentiating network; and means for dynamicallybounding the output of said differentiating network as a continuousfunction of variations in said input signal, so that the level of thedata received by said integrator does not exceed the level of the datarepresented by the input signal variations.
 2. An electrical filteraccording to claim 1 in whicH the means for dynamically bounding theoutput of said differentiating network includes a pair of half-waverectifiers respectively forming part of two signal paths each of whichis connected in essentially parallel relationship with saiddifferentiating network and each of which receives a portion of saidinput signal.
 3. An electrical filter according to claim 2 in which eachof the two signal paths which includes one of said pair of half-waverectifiers also includes a parallel diode-resistor combination shuntingthe particular half-wave rectifier included in that path.
 4. Anelectrical filter according to claim 3, further including an amplifier,a series resistor R, and a capacitor C shunting said amplifier, all ofsuch further components forming a common part of each of said two signalpaths, whereby the output characteristic Eo of the filter becomes(1/RwC)2 Ei where Ei is the input signal to said differentiatingnetwork.